A229075 Primes of the form p^2 + q^2 + 21, where p and q are consecutive primes.

191, 311, 479, 911, 1823, 2351, 4079, 5039, 6311, 8231, 9551, 10391, 13151, 14831, 17351, 22079, 24671, 33311, 35951, 41543, 51239, 57839, 61991, 69263, 73751, 76079, 84143, 101279, 103991, 106751, 111431, 115223, 141551, 145823, 198479, 210071, 223151, 263591

Offset

1,1

Comments

Conjecture: the expression p^2+q^2+c with p and q consecutive primes and c=21 generates more primes than any other value of c in the range 1..150. Hence, c=21 is considered for this sequence.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..5000

Example

a(1) = 191: prime(4)^2 + prime(4+1)^2 + 21 = 191, which is prime.

Maple

KD:= proc() local a; a:= ithprime(n)^2+ithprime(n+1)^2+21;  if isprime(a) then RETURN(a):  fi;  end: seq(KD(), n=1..300);

Mathematica

Select[Table[Prime[n]^2 + Prime[n + 1]^2 + 21, {n, 100}], PrimeQ] (* T. D. Noe, Sep 12 2013 *)

Crossrefs

Cf. A072669, A227340.

Sequence in context: A045141 A046010 A146361 * A367318 A142806 A142086

Adjacent sequences: A229072 A229073 A229074 * A229076 A229077 A229078

Keyword

nonn

Author

K. D. Bajpai, Sep 12 2013

Status

approved